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Article: α>(ϵ)=α<(ϵ) for the Margolus-Levitin quantum speed limit bound
Title | α>(ϵ)=α<(ϵ) for the Margolus-Levitin quantum speed limit bound |
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Authors | |
Issue Date | 1-Nov-2023 |
Publisher | American Physical Society |
Citation | Physical Review A (atomic, molecular, and optical physics and quantum information), 2023, v. 108, n. 5, p. 1-7 How to Cite? |
Abstract | The Margolus-Levitin (ML) bound says that for any time-independent Hamiltonian, the time needed to evolve from one quantum state to another is at least πα(ϵ)/2(E-E0), where (E-E0) is the expected energy of the system relative to the ground state of the Hamiltonian and α(ϵ) is a function of the fidelity ϵ between the two states. For a long time, only an upper bound α>(ϵ) and a lower bound α<(ϵ) are known, although they agree up to at least seven significant figures. Recently, Hörnedal and Sönnerborn [arXiv:2301.10063] proved an analytical expression for α(ϵ), a fully classified system whose evolution time saturates the ML bound, and gave this bound a symplectic-geometric interpretation. Here I solve the same problem through an elementary proof of the ML bound. By explicitly finding all the states that saturate the ML bound, I show that α>(ϵ) is indeed equal to α<(ϵ). More importantly, I point out a numerical stability issue in computing α>(ϵ) and report a simple way to evaluate it efficiently and accurately. |
Persistent Identifier | http://hdl.handle.net/10722/347316 |
ISSN | 2023 Impact Factor: 2.6 2023 SCImago Journal Rankings: 1.081 |
DC Field | Value | Language |
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dc.contributor.author | Chau, HF | - |
dc.date.accessioned | 2024-09-21T00:30:54Z | - |
dc.date.available | 2024-09-21T00:30:54Z | - |
dc.date.issued | 2023-11-01 | - |
dc.identifier.citation | Physical Review A (atomic, molecular, and optical physics and quantum information), 2023, v. 108, n. 5, p. 1-7 | - |
dc.identifier.issn | 2469-9926 | - |
dc.identifier.uri | http://hdl.handle.net/10722/347316 | - |
dc.description.abstract | <p>The Margolus-Levitin (ML) bound says that for any time-independent Hamiltonian, the time needed to evolve from one quantum state to another is at least πα(ϵ)/2(E-E0), where (E-E0) is the expected energy of the system relative to the ground state of the Hamiltonian and α(ϵ) is a function of the fidelity ϵ between the two states. For a long time, only an upper bound α>(ϵ) and a lower bound α<(ϵ) are known, although they agree up to at least seven significant figures. Recently, Hörnedal and Sönnerborn [arXiv:2301.10063] proved an analytical expression for α(ϵ), a fully classified system whose evolution time saturates the ML bound, and gave this bound a symplectic-geometric interpretation. Here I solve the same problem through an elementary proof of the ML bound. By explicitly finding all the states that saturate the ML bound, I show that α>(ϵ) is indeed equal to α<(ϵ). More importantly, I point out a numerical stability issue in computing α>(ϵ) and report a simple way to evaluate it efficiently and accurately.</p> | - |
dc.language | eng | - |
dc.publisher | American Physical Society | - |
dc.relation.ispartof | Physical Review A (atomic, molecular, and optical physics and quantum information) | - |
dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
dc.title | α>(ϵ)=α<(ϵ) for the Margolus-Levitin quantum speed limit bound | - |
dc.type | Article | - |
dc.identifier.doi | 10.1103/PhysRevA.108.052202 | - |
dc.identifier.scopus | eid_2-s2.0-85176091677 | - |
dc.identifier.volume | 108 | - |
dc.identifier.issue | 5 | - |
dc.identifier.spage | 1 | - |
dc.identifier.epage | 7 | - |
dc.identifier.eissn | 2469-9934 | - |
dc.identifier.issnl | 2469-9926 | - |